I know arcgis will use arcpy if its available. However arcgis AFAIK only works in Python 3.x Dont worry about the Desktop10.3 pth file, those would point at Python 2.7. In short, those shouldnt have anything to do with the problem.
– KHibmaMay 4 '18 at 17:27

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Can you confirm that you only have Anaconda (Python36), NOT ArcGIS Pro? Maybe its worth adding if you have ArcMap and what version.
– KHibmaMay 4 '18 at 17:30

Are you sure you imported arcpy before you called the module?
– reevesiiMay 4 '18 at 18:27

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Desktop arcpy only works with Python 2.7. If you want to use arcpy with Python 3 you need to install ArcGIS Pro. What you have installed is the "ArcGIS API for Python".
– user2856May 4 '18 at 22:49

1 Answer
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In ESRI's arcpy documentation "What is ArcPy" they make it sound like any other python package, but it is different than a other packages:

Apparently arcpy is closed source and only available within ESRI.

It seems to depend on ESRI's software

arcpy is not installed in Python, it's added to the python path if you have ESRI installed.

The package appears to be an interface to a local installation of ESRI, not a python package that uses python.

My conjecture is based on several readings. The clearest hints were from the blog of @Qiusheng-Wu. From this section about using Anaconda it seems clear that you're accessing python that's inside ESRI's program files:

Create a zconda.pth (path) file with the content “C:\Anaconda2\envs\arcpro\lib\site-packages” in it.

Then Copy zconda.pth to C:\Program Files\ArcGIS\Pro\bin\Python\envs\arcgispro-py3\lib\site-packages

It's confusing because you can install the packages esri and arcgis without the ESRI software (i.e. they're normal packages), but the same is not true of arcpy.

It's also confusing because the ESRI documentation makes it sound like this is a general purpose package without dependencies.

@Luke's answer in the comments is correct, but I wanted to provide a bit more documentation and actual answer for future searchers.